Matrices Associated with Classes of Arithmetical Functions Original Research Article

Let S = {x1, x2, ..., xn} be a Set of distinct positive integers. We investigate the structures, determinants, and inverses of n × n matrices of the form [β(xi, xj)], where β is in one of several classes of arithmetical functions. Among the classes we consider are Cohen′s class of even functions (mod r). We also study n × n matrices of the form [ƒ(xixj)] which have the arithmetical function ƒ(m) evaluated at the product of xi and xj as their i, j-entry, where ƒ is a quadratic function.